The work of [1]} was relatively small scale. The increased availability and resolution of remote-sensing instruments, coupled with the need to analyze the behaviour of entire ice sheets, led to work pioneering large-scale tractability for inference with Gau-Gau models. Developments were especially needed for the analysis of entire ice sheets. The papers of [2]} and [3]} are among the first to address this issue in a glaciological context. In particular, their focus was on Bayesian inference of large, spatial basal sliding fields at glaciers given surface velocity measurements. In both cases, the process and the observations were linked via a nonlinear function motivated by Stokes' ice flow equations, which were implemented using Taylor–Hood finite elements. The computational challenge addressed primarily in [2]} was how to efficiently sample from the posterior distribution when the dimensionality of the field is high (as in the case of the Antarctic ice sheets). Their solution was to use a Gaussian (Laplace) approximation [5]} of the posterior distribution over the basal sliding field, where the mean is set to the MAP estimate, and the precision matrix is set to the Hessian of the negative log of the posterior distribution, evaluated at the MAP estimate. For computational tractability, a low-rank approximation was used for the covariance matrix. [3]} used a strategy similar to that developed by [2]} to obtain a posterior distribution over the basal sliding field in Antarctica, which was then used to obtain a prediction interval for mass loss in Antarctica.
